Earlier this month, the Australian Bureau of Meteorology released the October figure for the Southern Oscillation Index (SOI). It showed a precipitous plunge of almost 20 points down to -14.6. Just how significant a drop this is can be seen in the chart below, which shows the distribution of monthly changes in the SOI going back to 1876 (-14.6 is at the lower 5% quantile, which means that a fall as big as this, or bigger, has only occurred 5% of the time).

**Distribution of SOI changes (Jan 1876-Oct 2009**)

But what exactly is the SOI and what is the significance of this decline in the index? The index is the standardised anomaly of the monthly average difference in sea-level air pressure between Tahiti and Darwin. “Standardised anomaly” means that the index measures the deviation of this pressure difference from the long-term average and is scaled by the standard deviation of the pressure difference and then multiplied by 10. The significance of the index lies in its relationship to the El Niño weather phenomenon. According to the Bureau of Meteorology:

Sustained negative values of the SOI often indicate El Niño episodes. These negative values are usually accompanied by sustained warming of the central and eastern tropical Pacific Ocean, a decrease in the strength of the Pacific Trade Winds, and a reduction in rainfall over eastern and northern Australia. The most recent strong El Niño was in 1997/98, although its effect on Australia was rather limited. Severe droughts resulted from the weak to moderate El Niño events of 2002/03 and 2006/07.

The chart below gives a historical perspective of the SOI over the last ten years. To get a better sense of the trends in the index, I have overlaid two different types of curve smoothing: a lowess (“locally-weighted scatterplot smoothing”) curve and a spline curve. The two give very similar results and make the 2002/03 and 2006/07 SOI downturns clearly visible. The timing of these downturns suggest that the corresponding droughts follow with something of a lag.

**Southern Oscillation Index (Jan 2000-Oct 2009**)

Over the last couple of years, the SOI has been solidly in positive territory and, again with a lag, there has followed an improvement in drought conditions. Indeed, New South Wales recently replaced the tight water restrictions which had been in place for a number of years with the less onerous “Water Wise” rules. Unfortunately, this change may turn out to have been premature. If the downward trend in the index seen over the last few months persists, Australia may face a return to severe drought conditions.

For anyone who is interested in how these charts were created, here is the R code. It is also available from the Stubborn Mule files section.

UPDATE: at the request of singingfish, here is a chart showing the full recorded history of the SOI back to 1876. The blue line is a spline smoothed curve.

**Southern Oscillation Index (1876-2009)**

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singingfishNice work!

I’d like to see an SOI graph from where records began, and a metric to determine the occurence of precipitous changes of the magnitude of the current one.

stubbornmulePost authorsingingfish:I have added a chart with the full history. As for a metric for the precipitousness of the most recent change, apart from the fact that the fall of 14.7 is in the lower 5% quantile, the standard deviation of monthly changes is 9, so the change represents a 1.6 standard deviation move. So, it’s a large move but certainly not unprecedented.JamesGloverIsnt the SOI as described above already scaled by the monthly std dev of pressure changes? So 14 is 14 SDs of something???

I’d get some data on rainfall and plot R^2 of SOI chgs vs rainfall deviation from that months l.t.average. By plotting R^2 vs delays 0, 1, 2 etc mths if BOM is correct this should rise and then fall off.

stubbornmulePost authorJamesGlover:the SOI is scaled by the standard deviation of the air pressure deviation. The standard deviation I referred to is the standard deviation of the monthly changes in the SOI to give a measure of how significant the 14.7 drop is, historically speaking.As far as the relationship to rainfall is concerned, the change in the SOI is not supposed to be the significant factor, it’s the outright value: negative values are often associated with El Niño events. Here is a chart of average annual SOI versus annual rainfall. It does show a rough correlation. I haven’t dug up monthly data at this stage.

JamesGloverIf SOI(k) = (P(k)-P_ave)/SD(P-P_ave) then SD(SOI)=1

JamesGloverAdding the following

var(SOI(k+1)-SOI(k))=var(SOI)-2r(k+1,k)var(SOI)+var(SOI)

=2var(SOI)(1-r(k+1,k))

=2(1-r(k+1,1)) where r(k+1,k) is the first autocorrelation const for t.s. SOI

so 0<=var(SOI(k+1)-SOI(k))<=4

and 0<=SD(dSOI))<=2

It doesnt seem SD(dSOI)=9 which is intuitively true also if SD(SOI)=1.

It is difficult doing maths directly in an edit box so be gentle if I have made a mistake!

stubbornmulePost authorJamesGlover:your reasoning would be impeccable but for the fact that I neglected to mention that the SOI is also (arbitrarily) scaled by a factor of 10. Your reasoning can then be adapted to show that 0<= sd(dSOI)) <= 20 and the standard deviation of 9 does indeed lie in this range. I have updated the post with a reference to the scaling factor.JamesGloverGlad we sorted that out – guess it was clear from SOI graph that SD(SOI)>>1.

singingfishas well as the rainfall data it would also be nice to look at the correlation with temperature data.